BARK optimizes black-box functions using Bayesian Additive Regression Trees.
problem Bayesian optimization of complex, black-box functions with uncertainty quantification.
method BART Kernel using tree agreement for posterior over piecewise-constant functions, explored using MCMC.
result BARK obtains samples of Gaussian processes for function distributions, enabling acquisition functions for optimization.
Function trees simplify complex ML models for better understanding.
problem Understanding and interpreting machine learning model predictions.
method Representing a multivariate function as a tree of simpler functions.
result Function trees reveal the global internal structure of functions.
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
Enhanced tree-based classifiers use derivatives and geometry for better function classification.
problem Improving classification of high-dimensional time series data.
method Integrates Functional Data Analysis with tree-based ensemble techniques, leveraging derivative and geometric features.
result Significant improvements over traditional approaches in function classification.
Flexible tree ensemble learning framework supports arbitrary loss functions and multi-task learning.
problem Limited modeling capabilities of existing tree ensemble learning toolkits.
method Differentiable tree ensembles with tensor-based formulation for efficient training.
result Our framework leads to 100x more compact and 23% more expressive tree ensembles.
Tree-based algorithm for functional data analysis reduces generalization error.
problem Classification and regression problems with functional data.
method Constrained convex optimization for weighted functional L2 space, multiple splitting rules, and weighted integral features. result Reduces generalization error while maintaining interpretability.
Decision trees algorithms use a gain function to select the best split during the tree's induction. This function is crucial to obtain trees with high predictive accuracy. Some gain functions can suffer from a bias when it compares splits of different arities. Quinlan proposed a gain ratio in C4.5's information gain fu…
Regression trees learn gradients of differentiable functions.
problem Understanding gradients of differentiable functions using regression trees.
method Developed a method to estimate gradients of differentiable functions using regression trees and exposed quantities from tree learning libraries.
result Gradient estimates from regression trees can be used to improve predictive analysis and solve tasks in uncertainty quantification.
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of rank-structured functions that can be seen as deep neural networks with a sparse arc…
New method learns binary decision trees efficiently.
problem Learning binary decision trees for data partitioning.
method Argmin differentiation for discrete and continuous parameters.
result Produces competitive binary trees with fast training.
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
problem Non-convex objective functions in simulation optimization.
method Integrates adaptive sampling with recursive partitioning of the search space.
result Proves global convergence and reliably identifies the global optimum.
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall output is the average of all leaves weighted by the gating values on their path. …
We introduce a novel boosting algorithm called `KTBoost' which combines kernel boosting and tree boosting. In each boosting iteration, the algorithm adds either a regression tree or reproducing kernel Hilbert space (RKHS) regression function to the ensemble of base learners. Intuitively, the idea is that discontinuous …
A novel gradient-based method optimizes decision trees for complex tasks.
problem Training decision trees with arbitrary differentiable loss functions.
method Gradient-based optimization using first and second derivatives of loss functions.
result Improves accuracy and flexibility in decision tree optimization.
Locally adaptive clustering for tree delineation.
problem Tree delineation from distance data.
method Locally adaptive hierarchical cluster termination.
result Multi-scale alternative to conventional termination criteria.
Boost-R uses gradient boosted trees for analyzing recurrence data.
problem Analyzing recurrence data with static and dynamic features.
method Gradient boosted additive trees with time-dependent functions.
result Estimates the cumulative intensity function of recurrent event processes.
Tree-based synthesis improves forecast accuracy in GDP and inflation.
problem Improving forecast accuracy in GDP and inflation.
method Developed a nonparametric synthesis function using regression trees.
result Tree-based synthesis leads to improved forecast accuracy.
Novel covariance function improves Bayesian optimization efficiency.
problem Efficient global optimization of expensive black-box functions.
method Additive tree-structured covariance function and parallel optimization algorithm.
result Significantly outperforms state-of-the-art methods in conditional parameter optimization.
Paper proves Łojasiewicz inequalities near simple bubble trees on surfaces.
problem Proving Łojasiewicz inequalities for critical points on surfaces.
method Deriving sufficient conditions for Łojasiewicz inequalities near almost-critical points in a Hilbert space.
result Sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree.
Enhances interpretability of functional survival models.
problem Lack of interpretability in functional survival models limits practical use.
method Introduces novel methods to enhance interpretability of FST and explainability of FRSF.
result Proposed methods yield efficient, easy-to-understand decision trees.
BART and MOTR-BART improve tree-based predictions with local linear models.
problem Non-linearity and high-order interactions in data.
method Bayesian Additive Regression Trees (BART) and Model Trees BART (MOTR-BART) using piecewise linear functions.
result MOTR-BART achieves equal or better performance with fewer trees than BART.
Study on unimodality of plucking polynomial with delay function.
problem Exploring unimodality of plucking polynomial with delay function.
method Presented a formula for the plucking polynomial of hedgehog rooted trees and explored unimodality with specific delay functions.
result Found interesting examples and speculations on unimodality of plucking polynomials with delay functions.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.
problem Optimal transport with multiple marginals and tree-structured quadratic costs.
method Tree-based Diffusion Schrödinger Bridge (TreeDSB) for continuous and dynamic solutions.
result TreeDSB efficiently computes Wasserstein barycenters in high dimensions.
Improved Bayesian optimization for conditional parameter spaces.
problem Efficient global optimization of expensive-to-evaluate functions in conditional parameter spaces.
method Additive tree-structured covariance function for conditional parameter optimization.
result Significantly improved sample-efficiency and wider applicability compared to existing methods.
Enhances functional classifier performance with new tree-based methods and unbiased feature importance assessment.
problem Challenges of high-dimensional functional data and biased feature importance assessment.
method Augmented functional classification trees and random forests with ad-hoc conditional permutations for unbiased feature importance.
result Significant enhancement in predictive power of functional classifiers through new feature importance assessment.
Paper studies ensemble probabilistic regression trees for smooth approximations.
problem Smooth approximations of regression functions.
method Ensemble versions of probabilistic regression trees.
result Ensemble probabilistic regression trees are consistent and perform well.
A new clustering algorithm for functional data using binary trees.
problem Clustering multivariate functional data with measurement errors.
method Recursive binary tree splitting for data clustering.
result Good performance in various complex settings, including vehicle trajectories.
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
Paper introduces methods to handle missing data in probabilistic regression trees.
problem Handling missing data in probabilistic regression trees.
method Three approaches: uniform probability, partial observation, and dimension-reduced smoothing.
result Preserves interpretability while extending applicability to incomplete datasets.
This paper optimizes high-dimensional oblique splits for decision trees, enhancing performance and computational efficiency.
problem Enhancing decision tree performance and computational efficiency in high-dimensional data.
method Established Sufficient Impurity Decrease (SID) convergence for s0-sparse oblique splits, proposing progressive trees for iterative refinement. result Demonstrated that SID function class expands with s0-sparsity, enabling capture of complex data-generating processes. Multivariate boosted trees improve forecasting and control by capturing correlated predictions.
problem Capturing multivariate target cross-correlations and applying structured penalties to predictions.
method A computationally efficient algorithm for fitting multivariate boosted trees.
result Multivariate trees outperform univariate counterparts in correlated prediction scenarios.
GAMI-Tree uses model-based trees to fit low-order fANOVA models.
problem Fitting interpretable fANOVA models with low-order interactions.
method GAMI-Tree uses model-based trees and a new interaction filtering method.
result GAMI-Tree outperforms EBM and GAMI-Net in predictive performance and interpretability.
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two numbers from its children and produces one output. Since thinking about functions in …
Novel loss functions improve decision tree learning from noisy data.
problem Training decision trees with noisy labels.
method Introducing distribution losses and a new negative exponential loss.
result The negative exponential loss leads to efficient and robust decision tree learning.
agtboost speeds up gradient tree boosting with automatic complexity adjustment.
problem Speeding up and simplifying gradient tree boosting computations.
method Adaptive gradient tree boosting with automatic complexity adjustment and feature importance.
result Significant decrease in computation time and simplification of model complexity.
Shallow trees in ensemble models make models more interpretable and sometimes better.
problem Lack of transparency in high-performing tree ensemble models.
method Developed an interpretation algorithm to convert tree ensembles into functional ANOVA representations. Proposed strategies to enhance interpretability.
result Shallow trees in ensemble models can lead to better generalization performance and improved interpretability.
Paper extends tree bijection for hyperbolic surfaces without requiring cusps.
problem Computing volumes and distances on hyperbolic surfaces without cusps.
method Extend tree bijection to half-tight cylinders, using Busemann function.
result Tree bijection can now be applied to surfaces without cusps.
Improved decision tree learning guarantees for complex functions.
problem Achieving provable guarantees for decision tree induction with complex target functions.
method Introduces a new splitting criterion that considers correlations between target function and subsets of attributes.
result Proves provable guarantees for all target functions with respect to the uniform distribution, circumventing previous impossibility results.
Variable selection for high-dimensional linear models has received a lot of attention lately, mostly in the context of l1-regularization. Part of the attraction is the variable selection effect: parsimonious models are obtained, which are very suitable for interpretation. In terms of predictive power, however, these re…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regr…
RST improves environmental time series classification accuracy using randomized B-spline trees.
problem Improving accuracy in classifying complex environmental time series.
method Randomized Spline Trees (RST) integrates randomized functional representations into ensemble learning.
result RST variants outperform standard Random Forests and Gradient Boosting on most environmental time series datasets.
Paper analyzes soft tree ensembles using NTK, finding only leaf count matters.
problem Understanding impact of various tree architectures in ensemble learning.
method Formulated and analyzed Neural Tangent Kernel (NTK) for soft tree ensembles.
result Only the number of leaves at each depth is relevant for tree architecture in ensemble learning.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning setting rather than the batch learning setting, and does not make use of soft splits…
Random Planted Forest interprets tree-based models by keeping some splits, leading to more interpretable predictions.
problem Estimating the unknown regression function from lower-order interaction terms.
method Modifying the random forest algorithm by keeping certain leaves instead of deleting them, resulting in non-binary trees called planted trees.
result The random planted forest achieves asymptotically optimal convergence rates up to a logarithmic factor when the interaction bound is low.
A new approach to Morse theory using folded ribbon trees.
problem Applying Morse theory on symmetric products of surfaces.
method Introducing an A-infinity category with objects as κ-tuples of Morse functions, and showing conditions for the endomorphism to be a Hecke algebra.
result The endomorphism of a specific type of κ-tuple of Morse functions on T*R^2 is the Hecke algebra associated to the symmetric group.
New method tests tree models without causing computational pressure.
problem Incompatibility of adversarial robustness testing with tree ensembles.
method Smooths tree ensembles with sigmoid functions and uses gradient descent.
result Successfully reveals adversarial vulnerability of tree ensemble models.